View
217
Download
0
Category
Preview:
Citation preview
Classifying Exchange Rate Regimes:
15 Years Later
Eduardo Levy-Yeyati and Federico Sturzenegger
CID Faculty Working Paper No. 319 June 2016
Copyright 2016 Levy-Yeyati, Eduardo; Sturzenegger, Federico; and the President and Fellows of Harvard
College
at Harvard University Center for International Development Working Papers
1
Classifying exchange rate regimes:
15 years later
Eduardo Levy-Yeyati, Federico Sturzenegger1
Abstract
Levy Yeyati and Sturzenegger (2001, 2003, 2005) proposed an exchange
rate regime classification based on cluster analysis to group countries
according to the relative volatility of exchange rates and reserves, thereby
shifting the focus from a de jure to de facto approach in the empirical
analysis of exchange rate policy. This note extends the classification
through 2014 and broadens the country sample, increasing the number of
classified country-year observations from 3335 to 5616. Based on this
extension, the note documents the main stylized facts in the 2000s,
including the behavior of exchange rate policy around the global financial
crisis, and the prevalence of floating regimes.
JEL classification: F30; F33
Keywords: Exchange rate regimes; fear of floating; fear of appreciation
1. Introduction
The analysis of the implications of alternative exchange rate regimes is
arguably one of the key questions in international economics, as well as one
with important measurement obstacles. Up until the late 90s most of the
empirical discussion on exchange rate regimes used the official (de jure)
regime classification that the IMF compiled based on the exchange rate
arrangements periodically reported by the country´s monetary authorities,
despite well-documented mismatches between reports and reality.
For
instance, it was recognized that many alleged floaters intervened in foreign
exchange markets so pervasively that, in terms of the exchange rate flexibility-
monetary autonomy mix, in practice they behaved closer to a conventional peg.
Conversely, many pegged regimes with autonomous (and often inconsistent)
1 Eduardo Levy Yeyati is Visiting Professor of Public Policy at Harvard Kennedy School of Government and professor at Universidad Torcuato Di Tella´s Business School. Federico
Sturzenegger is Governor of the Central Bank of Argentina, and professor at Universidad
Torcuato Di Tella´s Business School. The authors thank Quinto Van Peborgh for outstanding
research assistance.
2
monetary policies realigned the parity so often that they behave, for most
practical purposes, as floats.
These discrepancies –more precisely, the inadequate mapping of a
classification uniquely based on official reports on actual policies– tended to
mislead and ultimately frustrate empirical work in the field. Attempts to
identify the benign effect of pegs on chronic inflation or the link between
exchange rate flexibility and the depth of the business cycle were hampered
by miss-classification problems.2
A new approach to address this problem was preliminary outlined by
Ghosh et al, (1997) in light of the counterintuitive lack of empirical
association between inflation and pegs. The authors mitigated the
measurement bias by filtering out pegs that were realigned (devalued) more
than once a year.3 This useful shortcut, has a few drawbacks, particularly
in the description of non-pegs that displayed changes in both exchange
rate and the reserve stock: was the observed exchange rate variability large
relative to market pressure (as in a float) or small despite market pressure (as
in a massive but ultimately unsuccessful attempt to defend the fixed parity,
which in principle should be closer to a peg)?
Levy Yeyati–Sturzenegger (2001) introduced a first try to address these
concerns, building a de facto classification by comparing the relative
exchange rate and reserve volatilities.4 Underlying this choice was a textbook
definition of exchange rate regimes, whereby fixed regimes are associated with
changes in international reserves aimed at limiting the volatility of the
nominal exchange rate, and flexible regimes are characterized by stable reserves
and volatile exchange rates. The combined analysis of these three classification
variables should be sufficient, they argued, to assign regimes to a broad fix-
float grouping, independently of the country´s official report.5 This approach
was followed by other similar efforts, most notably by Reinhart and Rogoff
2 An interesting contrast was provided by the (at the time) relatively new literature on the
impact of a common currency on trade and economic performance (Frankel and Rose, 2000;
Rose, 2000). Since the presence of a common currency is easily verifiable, the empirical analysis
of currency unions was much more precise than that of other exchange rate regimes. 3 Frieden et al. (2001) also modified the standard IMF classification to account for frequent
adjusters and for different types of crawls for a group of selected countries. 4 More precisely, it identified exchange rate regimes based on the relative behavior of three
classification variables: changes in the nominal exchange rate, the volatility of those changes, and
the volatility of international reserve changes. 5 The paper clustered observations of three classification variables at a country-year level, and
assign them intuitively: the cluster with relatively high volatility of reserves and low
volatility in the nominal exchange rate was associated with pegs. Conversely, the cluster with low
volatility in international reserves and volatility in the nominal exchange rate was identified
with floats. Finally, countries with intermediate levels of volatility were labeled ―intermediates‖ –a
group that included, among others, economies with managed floats, binding exchange rate bands
and frequently realigned pegs.
3
(2002) and Shambaugh (2004), that combined de jure and de facto aspects to
characterize exchange rate policies more precisely.6 More recently, the IMF
replaced its traditional de jure classification by a subjective de facto one
prepared by its own country desks (Habermeier et al., 2009). These new de
facto classifications have delivered a large and growing body of literature
examining the determinants and consequences of exchange rate policy on many
macroeconomic variables.7
The new millennium has witnessed important developments regarding
exchange rate regimes: currency appreciation in most developing countries
coupled with the gradual decline in their net foreign currency liabilities,
transitorily interrupted by the global financial crisis; heavy leaning-against-the-
wind exchange rate intervention, including by formerly non-interventionist
countries like Israel or Switzerland; a gradual flexing of the Chinese peg. Are
we in the presence of a new paradigm that combines an inflation targeting or
inflation-centered policy with a more active management of the exchange rate?
Can we say that the new millennium marked the comeback of exchange rate
policies? More generally, how well known individual stories alter the regime
map when seen from a full global perspective? To address these questions and
to identify the new patterns, if any, of exchange rate policies in the 2000s, this
note updates Levy Yeyati–Sturzenegger´s (2001) and discusses the key
stylized results from the extended de facto classification.
The plan is as follows. Section 2 describes the additional data included in
this new exercise, briefly revisits the cluster methodology, and describes a
first characterization of regimes in the 2000s. Section 3 presents the
classification (described in more detail in Appendix C) and its main stylized
facts. Section 4 concludes.
2. Methodology
2.1. Classification variables
According to the textbook description, flexible exchange rates are
characterized by little intervention in the exchange rate markets together
with unlimited volatility of the nominal exchange rate. Conversely, a fixed
exchange rate regime occurs when the exchange rate does not move while
reserves are allowed to fluctuate. Under a crawling peg, changes in the nominal
6 In addition to providing a detailed story of exchange rate regimes at the country level, Reinhart
and Rogoff ―verified‖ the de jure regime: for example, a fixed exchange rate regime was verified if
the exchange rate was fixed; if not, it was reclassified into another category. In addition, they
considered the existence of dual exchange rates that used to be frequent in the developing world in
the past. Shambaugh, in turn, used a purely statistical approach similar to the LYS classification,
but base entirely on the volatility of the exchange rate. 7 See Levy Yeyati and Sturzenegger (2010) for a survey of the literature.
4
exchange rates occur with stable increments (i.e. low volatility in the rate of
change of the exchange rate) while active intervention keeps the exchange rate
along that path. Finally, a dirty float should be associated to the case in which
volatility is relatively high across all variables, with intervention only partially
smoothing exchange rate fluctuations.
With this in mind, regimes could be broadly characterized by the relative
behavior of three classification variables: the exchange rate volatility (σe),
measured as the average of the absolute monthly percentage changes in the
nominal exchange rate during a calendar year,8 the volatility of exchange rate
changes (σΔe), computed as the standard deviation of monthly percentage
changes in the exchange rate, and the volatility of reserves (σr).
To compute the first two variables we need to choose an appropriate
reference currency. In some cases this poses no problem (for example, we use
the U.S. dollar for the Mexican peso and the Deutsche Mark for the Italian
lira) but the reference currency is not always obvious (for example, for the
UK pound or the Swiss franc, the US dollar and the Deutsche Mark both
appear to be, a priori, equally good candidates). To sort out these ambiguous
cases we use the following criterion: if the country reports a peg we use the
legal peg currency; otherwise, we use the currency against which it exhibits
the lowest exchange rate volatility.9 Countries that peg to a basket are
eliminated from the sample unless the central peg parity or the basket
weights are disclosed.10
A list of the reference currencies used in each case is
reported in Appendix B.
Our third classification variable, the volatility of reserves (σr), requires
particular care. Reserves are notoriously difficult to measure, as there is
usually a difference between changes in reserves and the actual volume of
intervention.11
To approximate as closely as possible the change in reserves that
8 Choosing a calendar year as unit of account implies that in years where the exchange rate
regime changes, the yearly number will reflect a combination of both regimes. Argentina, for
example, implemented a fixed exchange rate in April of 1991. Our yearly data takes into
account the strong movements in the nominal exchange rate during the first three months of
the year and, as a result, the country is classified as a dirty float. Similarly Ecuador, which
dollarized in late January 2000 is classified as crawling peg for that year. This improves upon
IMF (1997) and Ghosh et al. (1997), which use the legal regime as of the end of each year. 9 For this exercise we considered the US dollar, the French franc, the German mark, the
British pound, the SDR, the ECU and the Japanese yen. For some small countries the
currency of a large neighbor was also considered. 10 If the basket is not known it is impossible to assess whether the country is intervening or not
to defend a predetermined parity. 11 See the careful discussion in Eichengreen et al. (1996) in the context of the European
Union. In addition, the timing of intervention is not always accurate, as central banks
economies with sophisticated foreign exchange markets tend to intervene using derivatives
such as currency futures or swaps, delaying and often smoothing out changes in the stock of
reserves.
5
reflects intervention in the foreign exchange market, we subtract government
deposits at the central bank from the central bank's net foreign assets.12
More
specifically, we define net reserves in U.S. dollars as:
where e indicates the price of a dollar in terms of local currency.13
Our measure
of the monthly intervention in the foreign exchange market, rt, is in turn
defined as
Finally, our volatility measure is computed as the average of the absolute
monthly change in net international reserves, rt,, relative to the monetary base
at the beginning of the month.14
Note that the use of both policy (intervention) and outcomes (exchange rate
changes) as classification variables is crucial to gauge the intensity of the
policy response. For example, a peg would respond to small exchange rate
shocks with small interventions, and to large shocks with large interventions.
Thus, a regime under a stable environment (small shocks) could be
misleadingly identified as a float based on interventions and as a peg based on
exchange rate volatility. Similarly, an exchange rate realignment as a result of
market pressure coupled with heavy intervention may be viewed as a float
12 Oil producing countries and countries with important privatization programs are examples of
cases where the latter correction matters. Calvo and Reinhart (2000) indicate other reasons
(hidden foreign exchange transactions, use of credit lines, derivative transactions, or issuance
of debt in foreign currency) that make it difficult to compute the real movement in reserves.
To these one could add coordinated intervention by other central banks (though this should be
limited to G-3 economies) and the measurement error introduced by the fact that all accounts
are transformed to dollar units: If the Central Bank holds a portfolio of assets with several
currencies, changes in the parities between the reserve currencies can be mistaken for foreign
exchange interventions. We believe this measurement error problem to be minor as most of the
reserves are in dollar denominated assets. 13 All central bank items are denominated in local currency and the time period for all variables
corresponds to the end of period for a specific month. 14 In practice we use line 11___ (or FASAF when available) from the IFS for foreign assets,
line 16c___ (or FASLF when available) for foreign liabilities and 16d___ (or FASLG when
available) for central government deposits. Line 14___ (or FASMB when available or14a__ if
previews options were not available) lagged one month is used as a measure of the monetary
base. Contrary to Calvo and Reinhart (2000) we use the changes relative to the monetary base
rather than the percentage change in reserves. We believe this is a better measure, as a given
percentage change in reserves in countries with low monetization implies a larger relative
intervention in forex markets.
6
based on exchange rates and as a peg based on reserves. In both cases, it is the
relative variation of policy and outcomes that better characterizes the true
reaction function underlying the regime.15
These three classification variables yield three-dimension country-year
observations for each of the IMF-reporting countries included in the sample
and each year of our time sample (1974-2013).16
Of the potential 7304
observations, 679 are left out due to undisclosed basket pegs and another 1437
lack data for at least one of the classifying variables, leaving a final sample of
5198 observations.
2.2. Classification procedure
We use cluster analysis to identify the regime groups based on the
previously described classification variables.17
Cluster analysis is a multivariate
procedure used to identify homogeneous groups of observations according to
similarities (distances) along certain quantitative dimensions, a natural approach
if the objective is to classify observations by comparison with other data points.
There are two approaches within the cluster analysis technique. Hierarchical
Cluster Analysis (HC), typically used for small samples, allows for some
additional discretion in determining the way distances are measured, in the
order the sample is introduced and in how the classification itself is
constructed. HC starts from a matrix of distances between pairs of elements
(the two closest are grouped in one cluster) and may differ in how distances
between clusters are estimated at successive steps. Alternatively, centroid
sorting (KMC; Anderberg, 1973) assign individual cases to the cluster with the
smallest distance between the case and the center of the cluster (centroid).
The number of clusters, K, is specified ex-ante by the user, and cluster centers
are iteratively estimated from the data. While HC seeks to unveil a nested
pattern or grouping of objects, KMC seeks to find the best K-group
classification of the observations with the least intervention from the
15 More important, we believe that the scope for interest rate policy to alter exchange market
conditions without a concomitant movement in reserves is quite limited, both in duration and
strength, as indicated by the lack of success of interest rate defenses against speculative attacks
during our sample period. However, many of the countries in our sample include cases in which
there may have been effective capital controls and/or segmented capital markets where interest
rate policy may have been a more feasible stabilization instrument. Yet, as is well known, the
literature has identified two channels through which this (sterilized) intervention can affect
interest rates: a signaling-expectation effect and a portfolio risk premium effect. 16 This still excludes some fixed exchange rate countries that are not IMF country members such as
Andorra, Liechenstein, Monaco, Nauru, Tuvalu and Vatican City, all of them fixed throughout the
post-Bretton Woods period (Tuvalu since 1979). See Obstfeld and Rogoff (1995). We also
exclude many semi-independent countries, dependencies or territories. On these see Rose
(2000). All other countries are included. 17 Refer to Levy Yeyati and Sturzenegger (2005) for a more extensive description.
7
researcher (only our definition of K is needed ex ante). Since it is crucial to
our work that the classification involves a minimal manipulation of the
classification criteria, we choose KMC as our cluster methodology.18
Once the three classification measures are computed for our universe of
countries, the KMC algorithm assigns the data to five different groups that
represent a distinct exchange rate regime (Table 1). Because KMC uses the
relative distance between points, it is important that all three measures
should be comparable. To that end, we first eliminate the two percent-upper
tail of observations for each of the three classification variables, which
excludes 226 outliers out of 5188 data points.19
We then z-normalize the
remaining 4962 observations and use the K-means algorithm to classify the
data into the five clusters described above.
In turn, since observations that display little variability along the three
variables cannot be assigned to any particular group at this stage, they are
labeled "inconclusives" and left unclassified.20
This initial, first-round
classification assigns 2050 data points and allocates a large number of
observations (2912 out of 4962) to the "inconclusive" category. While
variations in the classification variables within this group may be small
relative to the data points clustered in the first round, the data still displays
enough volatility to identify exchange rate regimes within the inconclusive
group. This is done in a second round using the same methodology as in the
first one. The second-round procedure assigns 1606 out of the 2912
inconclusive observations, leaving 1306 observations unclassified.
The distinction between first and second round, which mirrors
observations with high and low variability, provides an additional refinement
to the classification. By introducing this dimension, the methodology allows
to discriminate, albeit in a crude manner, the intensity of the shocks to which the
regime is subject, something that qualitative indexes previously used did not.
The classification algorithm is summarized in Figure 1.
18 The only restriction is that because the procedure is measure dependent all variables need to be z-
normalized. 19 Because these outliers do not present classification problems, we re-classify these
observations ex-post, by assigning them to the cluster with the nearest centroid. The 2%
threshold was chosen arbitrarily. Alternative values for this threshold delivered virtually
identical classifications. 20 If neither the nominal exchange rate nor reserves move, the exchange rate regime that the
country is actually implementing is not obvious from direct comparison with the rest of the
sample.
8
2.4. An extended classification
The methodology assigns an exchange rate regime to most data points in the
sample, and leave 1306 second-round inconclusives unclassified. Additionally,
the sample includes 1437 country-years for which some of the classification
variables were not available (Figure 2).
Table 2 shows, for each cluster, the central values as well as the upper and
lower bounds of the classification variables. Comparing the centroid values,
fixed regimes are characterized by relatively low nominal exchange rate
volatility (with an average absolute change of 0.60% per month as opposed to
1.59% in the case of floats), and high volatility in reserves (19.15% against
5.66% for floats). The two intermediate groups, on the other hand, exhibit
not only substantial intervention in the exchange rate market but also the
highest exchange rate volatility. This evidence suggests the following
important point: pure floats appear to tolerate relatively minor fluctuations in the
exchange rate. Conversely, as a rule, countries with substantial movements in
the nominal exchange rate usually intervene actively. The table also shows
that second round groups present less overlap between fixers and floaters.
While the former exhibit an absolute monthly volatility of the nominal
exchange rate that ranges from zero to 0.40%, the minimum exchange rate
volatility for the latter is 0.26%. Regarding international reserves, floaters
display an average absolute change ranging between 0.35% and 7.39% of the
monetary base, in contrast with a minimum reserve variability of 6.16% for
fixers.
Many of these unclassified observations can still be identified in an
uncontroversial fashion (e.g., Panama's or Ecuador´s unilateral dollarization or
Hong-Kong's currency board agreement). To include as many observations as
possible, we extend the classification using additional information on specific
countries left unclassified by the previous methodology. Specifically, a fixed
exchange rate regime is assigned to inconclusives that met one of these two
criteria: (i) exhibits zero volatility in the nominal exchange rate, or (ii) was
identified as a peg by the IMF and had an average volatility in the nominal
exchange rate smaller than 0.1% (placing them safely off-limits from the second
round-float and dirty-float clusters). 1131 out of the 1306 cases are classified as
pegged regimes in this way.
Using the same approach to identify pegs within the 1437 country-years
excluded due to lack of data, a total of 603 observations were added to the
final grouping.21
Importantly, this group includes 200 observations
21 Unclassified observations comprise pegs to undisclosed baskets (679) and inconclusive observations
(175) and countries with missing data (834).
9
corresponding to euro members, 187 of which were classified as floats and
13 as crawling peg. Extending the classification in this way brings up the
question about how to consider countries currently within the Euro zone.
Countries without a national currency pose a problem: should Greece, for
example, be regarded as California and classified as a float given how the
euro behaves relative to other currencies, or should the common currency be
the relevant aspect to classify the Greek regime as a peg? This is an open
question, the answer to which should depend on the issue at stake, and each
researcher can easily choose the approach as he sees fit. In our tables, we
choose the first option and classify these countries as we do with the euro as
a whole: float since 1998 (with the sole exception of an intermediate regime
in 2008). A useful analogy is the case of WAEMU, where we also classify
the regime of each member country according to the behavior of the
common currency –although because the common currency in this case is
fixed for the most part, there is less disagreement between the two
approaches).
Table 3 shows the final three-way distribution of observations into floats,
intermediate (including crawling pegs and dirty floats) and fixed regimes.
3. The prevalence of floating regimes
A first glance at the classification suggests that the steady decline in the
number of fixes since the demise of Bretton Woods accelerated during the
past decade. Figure 3 shows the relative importance of fixed, intermediate, and
floating regimes, and the trends towards exchange rate flexibility. While the
decline initially came from a lower number of fixed regimes (in most cases, a
Bretton Woods legacy), in recent years the reduction came at the expense of
intermediate regimes: more and more intermediates allow their exchange rates
to float more freely.
Figures 4 and 5 show that, with a predictable impasse during the global
financial crisis, the growing popularity of floats is explained largely by
exchange rate policies in high- and middle-income economies, while for low-
income economies pegs remained the preferred choice with only a limited
migration to floats prior to 2000. This is consistent with another significant
finding: the number of countries which run a fixed exchange rate regime without
explicitly stating that they do, ("fear of pegging", according to Levy Yeyati
and Sturzenegger, 2001) has increased remarkably over the last decade. The
same could be said of regimes that are officially but not de facto floating
(Calvo and Reinhart´s (2002) ―fear of floating‖). Overall, the prevalence of
floats among financially integrated economies goes in line with a declining
mismatch between words and deeds.
10
The shift to floats may also reflect the fact that increasingly global capital
markets have weakened even the strongest pegs in financially integrated
economies, forcing a steady movement to more flexible arrangements that,
crucially, involve discretionary intervention rather than a predetermined
parity. But appears at odds with the stability in the use of fixed regimes since
the early 90s, a point that challenges the view that increasing capital market
mobility was the driver behind the gradually abandonment of fixed
arrangements. More generally, the transition between intermediates and floats,
which reversed partially in the most recent period, may simply indicate that
exchange rate policy is endogenous to the local and the global contexts, and
swings between exchange rate stability and variability according to markets
pressure and whether deviations and high frequency volatility are seen as an
unnecessary source of nominal uncertainty.
4. Final remarks
The literature has, for the last 15 years, developed de facto alternatives to the
de jure exchange regime classifications. In this note we contribute to that end
by extending Levy Yeyati and Sturzenegger´s (2001) classification to the
present, and summarizing a few basic findings that emerge from a casual
inspection of the results.
11
References
Anderberg, M.R., 1973. Cluster Analysis for Applications. Academic Press, New York.
Calvo, G., Reinhart, C., 2000. Fear of floating. Quarterly Journal of Economics 117 (2),
379-408.
Eichengreen, B., Rose, A., Wyplosz, C., 1996. Speculative attacks on pegged exchange rates: An
empirical exploration with special reference to the European Monetary System. NBER
Working Paper No. 4898, NBER, Cambridge, MA.
Frankel, J., Rose, A., 2000. Estimating the effect of currency unions on trade and output. NBER
Working Paper No. 7857, NBER, Cambridge, MA.
Frieden, J., Ghezzi, P., Stein, E., 2001. Politics and exchange rate: A cross-country approach.
In: Frieden, J., Stein, E. (Eds.), The Currency Game: Exchange Rate Politics in Latin
America. IADB, Washington, DC.
Ghosh, A., Gulde, A., Ostry, J., Wolf, H., 1997. Does the nominal exchange rate regime
matter? NBER Working Paper No. 5874, NBER, Cambridge, MA.
Hartigan, J.A., 1975. Clustering Algorithms. John Wiley & Sons, Inc., New York.
Habermeier, K., Kokenyne. A., Veyrune, R., and Anderson, H., 2009. Revised System for the
Classification of Exchange Rate Arrangements,
Levy Yeyati, E., Sturzenegger, F., 2001. Exchange rate regimes and economic performance. IMF
Staff Papers 47, 62-98.
Levy Yeyati, E., Sturzenegger, F., 2003. To float or to fix: Evidence on the impact of exchange
rate regimes on growth. American Economic Review 93 (4), 1173-1193.
Levy Yeyati, Eduardo & Sturzenegger, F., 2010. "Monetary and Exchange Rate Policies," in Rodrik,
D. Handbook of Development Economics, Elsevier.
Obstfeld, M., Rogoff, K., 1995. The mirage of fixed exchange rates. NBER Working Paper No. 5191,
NBER, Cambridge, MA.
Rose, A., 2000. One money, one market? The effect of a common currency on international trade.
Economic Policy 30, 9-45.
12
Table 1
Classification criteria
o-e a Ae Crr
Inconclusive Low Low Low
Flexible High High Low
Dirty float High High High
Crawling peg High Low High
Fixed Low Low High
19
Figure 4. Developed and emerging countries (LYS classification).
Figure 5. Other Countries (LYS classification)
22
Appendix A. Description of the K-means cluster algorithm22
The following notation is used throughout this appendix unless otherwise stated:
NC Number of clusters requested
M i Mean of ith cluster
X k Vector of kth observation
d(xi,xi) Euclidean distance between vectors xi and xi
dmn mink/ d(Mi,Mi)
8 Convergence criteria
The computation involves three steps.
A.1. Selecting initial cluster centers
(a) If mini d(xk,Mi) > dmn and d(xk,Mm) > d(xk,Mn), then xk replaces Mn. If mini
d(xkMi) > dmn and d(xk,Mm) < d(xk,Mn), then xk replaces Mm; that is, if the distance
between xk and its closest cluster mean is greater than the distance between the two
closest means (Mm and Ma), then xk replaces either Mm and Mn, whichever is closer
to xk.
(b) If xk does not replace a cluster mean in (a), a second test is made:
Let Mq be the closest cluster mean to xk, and Mp be the second closest cluster
mean to xk. If d(xk,Mp) > mini d(Mq,Mi), then Mq = xk; that is, if xk is further from
the second closest cluster's center than the closest cluster's center is from any other
cluster's center, replace the closest cluster's center with xk.
At the end of one pass through the data, the initial means of all NC clusters are set.
A.2. Updating initial cluster centers
Starting with the first case, each case in turn is assigned to the nearest cluster,
and that cluster mean is updated. Note that the initial cluster center is
included in this mean. The updated cluster means are the classification cluster
centers.
A.3. Assign cases to the nearest cluster
The third pass through the data assigns each case to the nearest cluster, where
distance from a cluster is the Euclidean distance between that case and the (updated)
classification centers. Final cluster means are then calculated as the average values
of clustering variables for cases assigned to each cluster. Final cluster means do not
contain classification centers.
When the number of iterations is greater than one, the final cluster means in step 3
are set to the classification cluster means in the end of step 2, and step 3 is repeated
22Based on Hartigan (1975
23
again. The algorithm stops when either the maximum number of iterations is reached
or the maximum change of cluster centers in two successive iterations is smaller than
8 times the minimum distance among the initial cluster centers.
24
Appendix B. Currencies of reference
B . 1 T o t h e U S d o l l a r
Afghanistan, Algeria, Angola, Antigua and Barbuda (77-), Argentina, Armenia,
Aruba, Australia, Azerbaijan, Bahamas, Bahrain, Bangladesh (79-), Barbados (75-), Be-
larus (95-), Belize (77-), Bolivia, Brazil, Bulgaria (94-95), Burundi (74-83; 93-),
Cambodia, Canada, Chile (74-89;99-), China, Colombia, Democratic Republic of
Congo, previously Zaire, (74-75;83-), Costa Rica, Curacao & St. Maarten, Djibouti,
Dominica (79-), Dominican Republic, Ecuador, Egypt, El Salvador, Eritrea, Ethiopia,
Euro Area, The Gambia (86-), Georgia, Germany (74-98), Ghana, Grenada (77-),
Guatemala, Guinea (86-), Guyana (76-), Haiti, Honduras, Hong Kong, Hungary
(74-93), India (75-), Indonesia, Iran (74-80, 93-), Iraq, Israel, Jamaica, Japan,
Jordan (74; 88-), Kenya (74;87-), Korea, Kuwait, Kyrgyz Republic, Lao PDR,
Lebanon, Liberia, Libya (74-86), Lithuania (91-01), Macao, Malawi (74; 84-),
Malaysia, Maldives, Marshall Islands, Mauritania, Mauritius (83-), Mexico,
Micronesia, Mongolia, Mozambique, Nepal (74-84), Netherlands Antilles, New Zealand,
Nicaragua, Nigeria, Oman, Pakistan, Palau, Panama, Paraguay, Peru, Poland
(74-80), Qatar, Romania (74-03), Russia (74-04), Rwanda (74-82;94-), Sao Tome and
Principe, Saudi Arabia, Seychelles (96-), Sierra Leone (83-), Singapore, Solomon
Islands (83-), Somalia, South Africa, South Sudan, Sri Lanka, St. Kitts and Nevis
(77-), St. Lucia (77-), St. Vincent and the Grenadines (77-), Sudan, Suriname, Syrian
Arab Republic, Tajikistan, Tanzania (74; 79-), Thailand, Trinidad and Tobago (76-),
Turkey, Turkmenistan, Uganda (74-76; 81-), Ukraine, United Arab Emirates, United
Kingdom (74-86; 95-), Uruguay, Venezuela, Vietnam, Yemen, Zambia (74-75; 83-),
Zimbabwe.
B . 2 T o t h e B r i t i s h p o u n d
Antigua and Barbuda (74-76), Bangladesh (74-78), Barbados (74), Belize (74-76),
Dominica (74-78), The Gambia (74-85), Grenada (74-76), Guyana (74-75), India
(74), Ireland (74-78), Seychelles (74-78), Sierra Leone (74-78), St. Kitts and
Nevis (74-76), St. Lucia (74-76), St. Vincent and the Grenadines (74-76),
Trinidad and Tobago (74-75).
B.3 To th e Germa n ma rk (u n t i l 9 8 )
Albania, Austria, Belgium, Bosnia and Herzegovina, Bulgaria (96—), Croatia, Czech
Republic, Denmark, Estonia, Finland, France, Greece, Hungary (94-), Iceland, Ireland
(79—), Italy, Macedonia FYR, Moldova, Netherlands, Norway, Poland (80—),
Portugal, Slovak Republic, Slovenia, Spain, Sweden Switzerland, United Kingdom (87-
94), United States.
B.4 To the French f ranc (un t i l 98 )
25
Benin, Burkina Faso, Cabo Verde, Cameroon, Central African Republic, Chad, Co-
moros, Republic of Congo, Cote d'Ivoire, Equatorial Guinea, Gabon, Guinea Bissau (74-
77;84-), Madagascar, Mali, Morocco, Niger, Senegal, Togo, Tunisia, Vanuatu.
B.5. To the SDR
Burundi (84-92), Democratic Republic of Congo, previously Zaire, (76-82),
Guinea (74-85), Guinea Bissau (78-73) Iran (81-92), Jordan (75-87), Kazakhstan,
Kenya (75-86), Latvia (95-04), Libya (87—), Malawi (75-83), Mauritania,
Mauritius (74-82), Myanmar, Rwanda (83-93), Seychelles (79-95), Sierra Leone
(79-82), Tanzania (75-78), Uganda (77-80), Zambia (76-82).
B.6. To the Euro (from 1999)
Albania, Austria*, Belgium*, Benin, Bosnia and Herzegovina, Bulgaria*, Burkina Faso,
Cabo Verde, Cameroon, Central African Republic, Chad, Comoros, Republic of Congo,
Cote d'Ivoire, Croatia, Cyprus*, Czech Republic, Denmark, Equatorial Guinea, Estonia*,
Finland*, France*, Gabon, Germany*, Greece*, Guinea Bissau, Hungary, Iceland,
Ireland*, Italy*, Latvia (05-), Lithuania (02-), Luxembourg*, Macedonia FYR,
Malta*, Madagascar, Mali, Moldova, Montenegro, Morocco, Netherlands*, Niger,
Norway, Poland (80—), Portugal*, Senegal, Slovak Republic*, Romania (04-), Serbia
(02-), Slovenia*, Spain*, Sweden, Switzerland, Togo, Tunisia, United States.
B.7. Other
Bhutan, Indian Rupee
Brunei Darussalam, Singapore Dollar
Botswana, South African Rand
Chile (90-98), Central band parity as published by the Central Bank of Chile
Cyprus, ECU (90-98)
Fiji, Australian Dollar
Kiribati, Australian Dollar
Lesotho, South African Rand
Luxembourg (74-98), Belgium Franc
Malta (74-98), Italian Lira
Namibia, South African Rand
Nepal, Indian Rupee (85-)
Papua New Guinea, Australian Dollar
Russia (05-), Dual Currency Basket (Dollar-Euro)
San Marino, Italian Lira/Euro
Solomon Islands (74-82), Australian Dollar
Swaziland, South African Rand
Tonga, Australian Dollar
26
*Members of the Eurozone:
Joined in 1999: Austria, Belgium, Finland, France, Germany, Ireland, Italy,
Luxembourg, Netherlands, Portugal, Spain.
Joined in 2001: Greece.
Joined in 2007: Slovenia.
Joined in 2008: Cyprus, Malta.
Joined in 2009: Slovak Republic.
Joined in 2011: Estonia.
Recommended